Setrakian Industries needs to raise $48.5 million to fund a new project. The company will sell bonds that have a coupon rate of 5.56 percent paid semiannually and that mature in 10 years. The bonds will be sold at an initial YTM of 6.13 percent and have a par value of $2,000. How many bonds must be sold to raise the necessary funds?

Multiple Choice

48,500 bonds

24,250 bonds

64,243 bonds

25,317 bonds

31,646 bonds

To determine how many bonds Setrakian Industries must sell, we first need to calculate the price of a single bond. Then, we will divide the total amount of funds needed ($48.5 million) by the price of one bond.

Here are the key details provided:
- **Coupon rate**: 5.56% (annual, but paid semiannually)
- **YTM (Yield to Maturity)**: 6.13% (semiannual)
- **Maturity**: 10 years
- **Par value**: $2,000
- **Total funds needed**: $48.5 million

### Step 1: Semiannual Coupon Payment
The annual coupon payment is calculated as a percentage of the par value:
\[
\text{Annual Coupon Payment} = 0.0556 \times 2,000 = 111.20
\]
Since coupons are paid semiannually, the semiannual coupon payment is:
\[
\text{Semiannual Coupon Payment} = \frac{111.20}{2} = 55.60
\]

### Step 2: Number of Periods and YTM per Period
Since the bond pays interest semiannually and matures in 10 years, the number of periods (semiannual periods) is:
\[
N = 10 \times 2 = 20 \text{ periods}
\]
The semiannual yield (YTM per period) is half of the annual YTM:
\[
\text{Semiannual YTM} = \frac{6.13\%}{2} = 3.065\%
\]

### Step 3: Bond Price Formula
The price of a bond is the present value of the coupon payments and the present value of the face value (par value). The formula is:
\[
\text{Price} = \sum_{t=1}^{N} \frac{\text{Coupon Payment}}{(1 + r)^t} + \frac{\text{Par Value}}{(1 + r)^N}
\]
Where:
- $ N = 20 $
- $ r = 0.03065 $
- Coupon Payment = $55.60
- Par Value = $2,000

We can now calculate this price. Let me compute this.The price of one bond is approximately **$1,915.71**.

### Step 4: Calculate the Number of Bonds to be Sold
To raise $48.5 million, the company needs to sell:
\[
\text{Number of Bonds} = \frac{48,500,000}{1,915.71} \approx 25,317 \text{ bonds}
\]

Thus, the correct answer is **25,317 bonds**.

---

Would you like further details or clarification on any step?

Here are some related questions:
1. How would the bond price change if the coupon rate were higher?
2. How does a longer time to maturity affect the bond price?
3. What would happen to the number of bonds needed if the YTM increased?
4. How are the semiannual and annual YTMs related in bond pricing?
5. How is bond duration related to its price sensitivity?

**Tip:** Bond prices and yields are inversely related: as yields increase, bond prices decrease, and vice versa.

Setrakian Industries needs to raise $48.5 million to fund a new project. The company will sell bonds that have a coupon rate of 5.56 percent paid semiannually and that mature in 10 years. The bonds will be sold at an initial YTM of 6.13 percent and have a par value of $2,000. How many bonds must be sold to raise the necessary funds?

Learn how to calculate the number of bonds Setrakian Industries must sell to raise $48.5 million. The bonds have a coupon rate of 5.56% (paid semiannually) and are sold at a yield to maturity (YTM) of 6.13%. Understand bond pricing, semiannual payments, and the effect of YTM on bond valuation. Suitable for finance students.

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